Nurturing reflective learners in mathematics [electronic resource] . Yearbook 2013 : Association of Mathematics Educators / Berinderjeet Kaur, editor.

Format:

Book

Contributor:

Kaur, Berinderjeet, 1955-

Language:

English

Subjects (All):

Mathematics--Study and teaching.

Mathematics.

Mathematics teachers.

Physical Description:

1 online resource (326 pages)

Edition:

1st ed.

Place of Publication:

Singapore : World Scientific, c2013.

Contents:

Intro

Contents

Chapter 1 Nurturing Reflective Learners in Mathematics: An Introduction Berinderjeet KAUR

1 Introduction

2 Fundamentals for Nurturing Reflective Learners

3 Instructional Tools for Nurturing Reflective Learners

4 Approaches to Teaching for Nurturing Reflective Learners

5 Some Concluding Thoughts

References

Chapter 2 The Neurocognition of Reflection: The Mystery in Learning, the Essence of Teaching, From Mystery to Mastery Frank Chee Tet VOON

2 How Do We Really Learn?

3 The Two Phases of Understanding and Recall

4 Neuroanatomy

5 Neural Pathways

6 Wiring and Firing Together

7 The Myelin Sheath

8 New and Emerging Ideas in Neurocognition

9 Deep Practice

10 Neuronal Networks

11 An Analogy of Learning Paths as Learning New Routes of Travel

12 An Example of Collaborative Learning

13 Use of Technology

14 Neurocognition, Learning and Mastery

15 Conclusion

Acknowledgements

Appendix

Chapter 3 Working with the Whole Psyche: Nurturing Reflective Learners John MASON

2 Approach

3 Preliminary Tasks

3.1 Arithmetical relations &amp

properties

3.2 Recognition11

4 Interlude on the Structure of the Psyche

5 Mathematical Themes

5.1 Doing &amp

undoing additively

5.2 Doing &amp

undoing unexpectedly

5.3 Doing &amp

undoing multiplicatively

5.4 Reflections

6 Geometry as Context

6.1 Alternating sums of squares

6.2 More alternating sums of squares

6.3 The carpet theorem

7 Area and Perimeter as Context

7.1 More or less (perimeter and area)

8 Recognising Types of Numbers as Context

8.1 Four consecutive sums

8.2 Consecutive sums

8.3 One more than the product of four consecutive numbers

8.4 Sundaram's grid

8.5 Generalising patterns from 2.

9 Reflection on Nurturing Reflection

Chapter 4 Knowledge and Beliefs for Nurturing Reflective Learners of Rational Number Concepts Kim BESWICK

2 Teacher Knowledge and Nurturing Reflective Learners

3 Teacher Beliefs and Nurturing Reflective Learners

4 Learning Rational Number Concepts

5 Examples of Reflective Learning

5.1 Understanding one third: Year 2

5.2 Comparing fractions: Year 5

5.3 Understanding equivalent fractions: Year 7

6 Reflective Learners and the Teacher Knowledge and Beliefs that Support Them

7 Conclusion

Acknowledgement

Chapter 5 Metacognitive Reflection at Secondary Level WONG Khoon Yoong

1 Introduction: Two Aspects of Metacognition

2 Metacognition During Problem Solving

2.1 Metacognitive processes and metacognitive questions

2.2 Local studies about problem solving behaviours

2.3 Teaching metacognition

3 Equip Students to Regulate their Learning

3.1 Local studies about learning strategies in mathematics

3.2 Teaching self-regulation of learning

4 Concluding Remarks

Chapter 6 Reflecting on an Excellent Teacher's Video Recorded Mathematics Lesson: What Can We Learn? LIM Chap Sam CHEW Cheng Meng

2 Review of Literature

2.1 Reflection and reflective thinking

2.2 Importance of reflective thinking for teachers

2.3 Possible methods used for reflective thinking

3 The Study

3.1 The participants

3.2 Data collection

3.3 Data analysis and discussion

4 Implications and Conclusion

Chapter 7 Learning from Student Reflections Barry KISSANE

2 Review of the Literature

3 Two Assessment Tasks Involving Reflection

3.1 Reflections on learning

3.2 Reflections on learning with technology

4 Selected Themes Emerging.

4.1 Personal histories and emotions

4.2 Assessment

4.3 Rules of thumb

4.4 When are we gonna use this?

4.5 The one right way

4.6 Mental arithmetic

4.7 It's simple

4.8 Visual learners

4.9 Virtual manipulatives

4.10 Calculators

4.11 Understanding mathematics?

5 Conclusion: Reflecting on Reflections

Chapter 8 Reflecting on Calculation: When Drilling Becomes Fulfilling Anne WATSON

2 Where to Look for Patterns

3 Shifting to Deductive Reasoning

3.1 Task 1

3.2 Task 2

3.3 Task 3

3.4 Task 4

3.5 Task 5

3.6 Task 6

4 Reflecting on the Design of the Tasks

5 Summary

Chapter 9 Developing Reflective Learners Through Solving Non-Routine Problems Marian KEMP

2 Overview of Problem Solving

3 Developing Reflective Learners

4 Choosing Problems to Develop Reflective Thinking

4.1 Guidelines for selecting problems

4.2 Three examples of the guidelines in use

5 Conclusion

Acknowlegement

Chapter 10 Mathematics Competition Questions and Mathematical Tasks for Instructional Use TOH Tin Lam

2 Mathematical Tasks and Competition Questions

3 Developing Students' Interest in Mathematics

3.1 Illustration 1: Compute using algebraic formulae

3.2 Illustration 2. Compute using basic algebraic / arithmetic rules

3.3 Illustration 3. Game based on a competition question

4 Developing Students' Higher Order Thinking

4.1 Challenging students' understanding of mathematical steps to solve an algebraic equation

4.2 Challenging students' understanding of mathematical reasoning

5 Some Valuable "Obsolete" Questions in Mathematics Competitions

6 Some Final Remarks

References.

Chapter 11 Mathematical Tasks in the Advanced Mathematics Class for Nurturing Reflection Oh Nam KWON Ji Eun LEE

1.1 Advanced mathematics - A new challenge for the mathematics teacher in Korea

1.2 The necessity and importance of learning polar coordinates

2 Reflective Thinking and Reflective Learning

2.1 Reflective thinking

2.2 Cognitive disequilibrium for reflective thinking

2.3 Mathematical tasks for cognitive disequilibrium

2.4 The main stages of a process of reflective thinking

3 Mathematical Tasks

3.1 System of equations in polar coordinates

3.2 Symmetry of polar graph

4 Conclusion

Chapter 12 Using Codes to Facilitate Metacognition in Mathematics WONG Oon Hua

2 Literature Review

3 A Study on the Use of Codes for Grading Mathematics Assignments

3.1 Devising the codes

3.2 Implementing the codes

3.3 Data collection and findings

4 Some Considerations for the Use of Codes

5 Conclusions

Chapter 13 Mathematics Lessons Stimulating Reflective Learning: Japanese Perspective Keiko HINO

2 Teaching Mathematics in the Classroom: Problem Solving Approach

2.1 Japanese lesson pattern

2.2 Critical roles played by teacher in the structured problem solving

3 Stimulating Reflective Thinking and Learning through Structured Problem Solving

3.1 Perspectives on stimulating children's reflective thinking and learning

3.2 An example: Compare the crowdedness of four rabbit cages

4 Examples from Practice-Based Studies: Teachers' Trials in an In-Service Education Program

4.1 Providing a foothold

4.2 Stimulating reflection through interaction

Chapter 14 Insights from Students' Process of Understanding Mathematics for Nurturing Reflective Learners Masataka KOYAMA

2 The "Two-Axis Process Model" of Mathematical Understanding

3 Development of a 8th Grade Lesson on "Regular Stellar Polygon"

3.1 Objectives of the lesson

3.2 A brief of the lesson

4 Qualitative Analysis of Students' Process of Mathematical Understanding in the Lesson

4.1 Three tasks posed by the teacher

4.2 Solution process of task 1

4.3 Solution process of task 2

4.4 Transition from task 2 to task 3

Notes

Chapter 15 Mathematics Learning Episode that Promotes Reflective Thinking Among Elementary Pupils Auxencia Alarcon LIMJAP

2 Learner Centered Learning Environment

2.1 Identifying the students' prior knowledge

2.2 Providing engaging interactions

2.3 Coaching students' transformation and mastery

2.4 Evaluating and verifying students' performance

3 LCLE Learning Episode on Fractions

3.1 Eliciting students' understanding of subtraction of fractions

3.2 Providing tasks on subtracting mixed number from whole number

3.3 Assessing learning to coach students' transformation and mastery

4 Reflective Thinking in a Procedural Task

4.1 Representations and reflections in dyads

4.2 Manifestations of reflective thinking

Appendix A

Appendix B

Contributing Authors.

Notes:

Description based on publisher supplied metadata and other sources.

Includes bibliographical references.

Other Format:

Print version: Kaur, Berinderjeet Nurturing Reflective Learners In Mathematics: Yearbook 2013, Association Of Mathematics Educators

ISBN:

9789814472760

OCLC:

843874036